College

Karissa begins to solve the equation [tex]\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)[/tex]. Her work is shown below:

[tex]
\begin{array}{c}
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4) \\
\frac{1}{2} x-7+11=\frac{1}{2} x-x+4 \\
\frac{1}{2} x+4=-\frac{1}{2} x+4 \\
\end{array}
[/tex]

When she subtracts 4 from both sides, [tex]\frac{1}{2} x=-\frac{1}{2}[/tex] results. What is the value of [tex]x[/tex]?

A. [tex]-1[/tex]

B. [tex]-\frac{1}{2}[/tex]

C. [tex]0[/tex]

D. [tex]\frac{1}{2}[/tex]

Answer :

Let's solve the given equation step-by-step to find the value of [tex]\( x \)[/tex].

We are starting from this equation after Karissa's work:

[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]

First, let's subtract 4 from both sides to simplify the equation:

[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]

Now, to isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:

[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]

This simplifies to:

[tex]\[
x = -1
\][/tex]

So, the value of [tex]\( x \)[/tex] is [tex]\(-1\)[/tex].

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